The present invention relates to an apparatus for and a method of measuring period jitter that are applied to a measurement of jitter of, for example, a microprocessor clock.
A time interval analyzer and/or an oscilloscope have conventionally been used for the measurement of period jitter. The method of these apparatus is called Zero-crossing Method, in which, as shown in FIG. 1, a clock signal (a signal under measurement) x(t) from, for example, a PLL (Phase-Locked Loop) under test 11 is supplied to a time interval analyzer 12. Regarding a signal under measurement x(t), a next rising edge following one rising edge fluctuates against the preceding rising edge as indicated by dotted lines. That is, a time interval Tp between the two rising edges, namely a period fluctuates. In the Zero-crossing Method, a time interval between zero-crossings (period) of the signal under measurement is measured, a fluctuation of period is measured by a histogram analysis, and its histogram is displayed as shown in FIG. 2. A time interval analyzer is described in, for example, “Phase Digitizing Sharpens Timing Measurements” by D.Chu, IEEE Spectrum, pp. 28-32, 1988, and “A Method of Serial Data Jitter Analysis Using One-Shot Time Interval Measurements” by J. Wilstrup, Proceedings of IEEE International Test Conference, pp. 819-823, 1998.
In addition, Tektronix, Inc. and LeCroy Co. have recently been providing digital oscilloscopes each being able to measure a jitter using an interpolation method. In this jitter measurement method using the interpolation method (interpolation-based jitter measurement method), an interval between data having signal values close to a zero-crossing out of measured data of a sampled signal under measurement is interpolated to estimate a timing of zero-crossing. That is, in order to measure a fluctuation of period, a time interval between zero-crossings (period) is estimated using a data interpolation with a small error.
That is, as shown in FIG. 3, a signal under measurement x(t) from the PLL under test 11 is inputted to a digital oscilloscope 14. In the digital oscilloscope 14, as shown in FIG. 4, the inputted signal under measurement x(t) is converted into a digital data sequence by an analog-to-digital converter 15. A data-interpolation is applied to an interval between data having signal values close to a zero-crossing in the digital data sequence by an interpolator 16. With respect to the data-interpolated digital data sequence, a time interval between zero-crossings is measured by a period estimator 17. A histogram of the measured values is displayed on a histogram estimating part 18, and a root-mean-square value and a peak-to-peak value of fluctuations of the measured time intervals are obtained by an RMS & Peak-to-Peak Detector 19. For example, in the case in which a signal under measurement x(t) has a waveform shown in FIG. 5A, its period jitters are measured as shown in FIG. 5B.
In the jitter measurement method by the time interval analyzer method, a time interval between zero-crossings is measured. Therefore a correct measurement can be performed. However, because this method repeatedly measures jitter but includes an intermediate dead-time between measurements, there is a problem that it takes a long time to acquire a number of data that are required for a histogram analysis. In addition, in an interpolation-based jitter measurement method in which a wide-band oscilloscope and an interpolation method are combined, there is a problem that a histogram of jitter cannot accurately be estimated, and a jitter values are overestimated (overestimation). For example, for a 400 MHz clock signal the time interval analyzer method measure a root-mean-square value of jitter as 7.72 ps while the interpolation method measures, a root-mean-square of 8.47 ps, that is larger than the value estimated by the time interval analyzer method.
On the other hand, inventors of the present invention have proposed a method of measuring a jitter as described below in an article entitled “Extraction of Peak-to-Peak and RMS Sinusoidal Jitter Using an Analytic Signal Method” by T. J. Yamaguchi, M. Soma, M. Ishida, and T. Ohmi, Proceedings of 18th IEEE VLSI Test Symposium, pp. 395-402, 2000. That is, as shown in FIG. 6, an analog clock waveform from a PLL (Phase locked loop) circuit under test 11 is converted into a digital clock signal xc(t) by an analog-to-digital converter 22, and the digital clock signal xc(t) is supplied to a Hilbert pair generator 24 acting as an analytic signal transforming part 23, where the digital clock signal xc(t) is transformed into an analytic signal zc(t).
Now, a clock signal xc(t) is defined as follows.xc(t)=Accos(2πfct+θc−Δφ(t))The Ac and the fc are nominal values of amplitude and frequency of a clock signal respectively, the θc is an initial phase angle, and the Δφ(t) is a phase fluctuation that is called an instantaneous phase noise.
Signal components around a fundamental frequency of the clock signal xc(t) are extracted by a bandpass filter (not shown) and are Hilbert-transformed by a Hilbert transformer 25 in the Hilbert pair generator 24 to obtain the following equation.{circumflex over (X)}c(t)=H[Xc(t)]=Acsin(2πfct+θc−Δθ(t))Then, an analytic signal zc(t) having xc(t) and {circumflex over (x)}c(t) as a real part and an imaginary part, respectively, is obtained as follows.                                           z            c                    ⁡                      (            t            )                          =                ⁢                                            x              c                        ⁡                          (              t              )                                +                      j            ⁢                                                   ⁢                                                            x                  ^                                c                            ⁡                              (                t                )                                                                            =                ⁢                                            A              c                        ⁢                          cos              ⁡                              (                                                      2                    ⁢                                                                                   ⁢                    π                    ⁢                                                                                   ⁢                                          f                      c                                        ⁢                    t                                    +                                      θ                    c                                    -                                      Δ                    ⁢                                                                                   ⁢                                          φ                      ⁡                                              (                        t                        )                                                                                            )                                              +                      j            ⁢                                                   ⁢                          A              c                        ⁢                          sin              ⁡                              (                                                      2                    ⁢                                                                                   ⁢                    π                    ⁢                                                                                   ⁢                                          f                      c                                        ⁢                    t                                    +                                      θ                    c                                    -                                      Δ                    ⁢                                                                                   ⁢                                          φ                      ⁡                                              (                        t                        )                                                                                            )                                                        
From this analytic signal zc(t), an instantaneous phase Θ(t) of the clock signal xc(t) can be estimated by the instantaneous phase estimator 26 as follows.Θ(t)=[2πfct+θc−Δφ(t)]mod 2π[rad]A linear phase is removed from this instantaneous phase Θ(t) by a linear phase remover 27 to obtain a phase noise waveform Δφ(t). That is, in the linear phase remover 27, a continuous phase converting part 28 applies a phase unwrap method to the instantaneous phase Θ(t) to obtain a continuous instantaneous phase θ(t) as follows.θ(t)=2πfct+θc−Δφ(t)[rad]The phase unwrap method is shown in “A New Phase Unwrapping Algorithm” by Jose M. Tribolet, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-25, pp. 170-177, 1977 and in “On Frequency-Domain and Time-Domain Phase Unwrapping” by Kuno P. Zimmermann, Proc. IEEE. vol. 75, pp. 519-520, 1987.
An instantaneous linear phase of a continuous instantaneous phase θ(t), i.e., a linear instantaneous phase [2πfct+θc] of a jitter-free ideal signal is estimated by a linear phase evaluator 29 using a linear trend estimating method. That is, an instantaneous linear phase of a continuous instantaneous phase θ(t) is estimated by applying a linear line fitting by least squares method to the above continuous phase θ(t). This estimated linear phase [2πfct+θc] is subtracted from the continuous phase θ(t) by a subtracting part 31 to obtain a variable term Δφ(t) of the instantaneous phase Θ(t), i.e., an instantaneous phase noise waveform as follows.θ(t)=Δφ(t)The instantaneous phase noise waveform Δφ(t) thus obtained is inputted, after having been sampled by the zero-crossing sampler 34, to a peak-to-peak detector 32 as a timing jitter sequence Δφ[n], where a difference between the maximum peak value max (Δφ[k]) and the minimum peak value min (Δφ[k]) of the Δφ[n] (=Δφ(nT)) is calculated to obtain a peak value (peak-to-peak value) Δφpp of timing jitter as follows.       Δ    ⁢                   ⁢          ϕ      pp        =                    max        k            ⁢              (                  Δ          ⁢                                           ⁢                      ϕ            ⁡                          [              k              ]                                      )              -                  min        k            ⁢              (                  Δ          ⁢                                           ⁢                      ϕ            ⁡                          [              k              ]                                      )            In addition, the timing jitter sequence Δφ[n] is also inputted to a root-mean-square detector 33, where a root-mean-square (RMS) value of the timing jitter sequence Δφ[n] is calculated using following equation to obtain a root-mean-square value ΔφRMS of timing jitters.       Δ    ⁢                   ⁢          ϕ      MRS        =                    1        N            ⁢                        ∑                      k            =            0                                N            -            1                          ⁢                  Δ          ⁢                                           ⁢                                    ϕ              2                        ⁡                          [              n              ]                                          
This method is referred to as the Δφ method, since a peak value of timing jitter (peak-to-peak value) and a root-mean-square value of timing jitters are obtained from the instantaneous phase noise waveform Δφ(t). Further, an instantaneous phase noise waveform Δφ(t) is sometimes written as a instantaneous phase noise Δφ(t) or a phase noise waveform Δφ(t).
According to the Δφ method, a timing jitter can be measured at high speed with relatively high accuracy.
It is an object of the present invention to provide an apparatus for and a method of measuring a jitter that can measure a period jitter in a short period of time and with high accuracy, namely an apparatus for and a method of measuring a jitter that can measure jitter values compatible with those measured by the conventional time interval analyzer method.